| R. B. Ash. Information Theory. Dover, 1965. |
....there are several reasons to think of it as a good measure of uncertainty. Perhaps the most important of these is that it quantifies the number of binary valued questions one expects to ask (per instance of H) if one s only means to ascertain the outcome is from a colleague who knows the result [81]. Under this quantification, the lower the Shannon entropy, the more predictable a measurement s outcomes. Because the function f(x) x log x is concave on the interval [0, 1] it follows that, log # P (h d) log P (h d) P (d)S(H d) 76) Indeed we hope to find a ....
R. B. Ash, Information Theory, (Dover, New York, 1965).
....optimal, and the best error exponent is L. 54 Remark: Our approach generalizes in a straightforward manner for stationary Markov sources that contain one irreducible essential class C1 and an arbitrary number of inessential classes C2, C8. Such a Markov source is said to be indecomposable [7]. In this case, the stationary distribution is r = rl, 0, 0) where rl is the station ary distribution corresponding to C1 and the zeros correspond to inessential classes. We have the following result. Corollary 3.4 Let X1, X2, be a stationary Markov source generated according to p( ....
R. B. Ash, Information Theory, Dover Publications, New York, 1965.
.... to the natural interpretation of Shannon entropy as the expectation of a random variable that takes values log(f(X) with probability f(X) An alternative interpretation is that it is the minimum average number of yes or no questions required to determine the result of one observation of X [3]. This entropy function takes its largest value when all possible values of X have the same probability of being observed, and the smallest when all of the probability mass is concentrated on a single value. Shannon entropy has been considered as a distortion measure by other authors (see [17] ....
R. B. Ash. Information Theory. Dover Publication, Inc., New York, 1965.
....z, z and y respectively and let E be the probability space that models the eavesdropper s information on z. Then, the following inequality holds Z; E; Y ) I(Z; E) 8) whenever det H 6= 0; 9) where H = H 2 H 1 ] Proof of the lemma. By very well known information theoretic relations [1] we have Z; E; Y ) I( Z; Y ) I( Z; EjY ) 10) Let us prove first that if eq. 9) were true, then I( Z; Y ) 0. Consider the joint probability Prob[ z; y] Prob[zH ] The condition (9) implies that H is a non singular ( r) r) matrix and therefore Prob[ z; y] Prob[z ....
.... symbol error probability m and check symbols through noiseless channel can be considered as a transmission of both groups of symbols over time sharing channel with the capacity C ts = k r Cm (19) where Cm = 1 H( m ) Substitution of (19) in Shannon s condition of reliable communication [1] gives R = C ts which implies the condition r k H( m ) Taking into account that asymptotically [2] t c (1 H( m ) k we get from eq. 7) the condition on key rate R k = to provide an exponential decreasing of information I 0 leaking to eavesdropper, as k 1 R k H( w ) H( m ) ....
Ash, R.B. "Information Theory". Dover, New York, 1990.
....the relevance between two kernel documents. The weight w i for a base vector document b i is calculated using the following equation: where n i is the number of related documents for b i and N is the total number of kernel documents. This weight measurement method is based upon information theory [3], and is similar to the weight measure employed by Wilbur et al.[4] to evaluate the significance of a specific keyword in determining the relatedness of two papers. Vector Representation of a Kernel Document Assuming that there are M base vectors documents, b 1 , b 2 , b M , and the weight ....
Ash R: Information Theory. Chapter 1. Dover Publishers 1990
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R. B. Ash. Information Theory. Dover, 1965.
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R. B. Ash. Information Theory. Dover Publications, New York, NY, 1990.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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Robert B. Ash. Information Theory. Dover, New York, 1965.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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R. B. Ash. Information Theory. Dover Publications, New York, NY, 1990.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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Ash, R. B. Information Theory, Dover, London (1965).
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R. B. Ash, Information Theory. John Wiley & Sons, Inc., 1967.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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Ash, R, B. (1965) Information Theory, Dover, New York.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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R. Ash, Information theory, Dover publications, New-York, 1965.
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Ash, R. Information Theory. Wiley-Interscience, New York, 1965.
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R. Ash "Information Theory," Dover Publications, Inc, New York, 1965.
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R. B. Ash. Information Theory. Dover, 1965.
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